161-246 Reasoning and Uncertainty

161-115 Introduction to Formal Logic or permission from the Head of Department or the subject coordinator, 620-122 Mathematics B (Advanced) or 620-142 Mathematics B or 433-255 Logic and Computation or 620-211 Mathematics 2 (Advanced).

The distinction between good and bad reasoning ought to apply whether we are certain of our premises or not. However, many of the important techniques in contemporary logic were developed to model the kinds of proof found in mathematical reasoning, where certainty seems available and proofs guarantee their conclusions. This course examines the different kinds of reasoning appropriate where uncertainty is rife. This course will consider techniques from among elementary probability theory, Bayesian decision theory, inductive inference, game theory, fuzzy logic, non-monotonic reasoning, default inference, dynamic logic and rational belief revision. Students will be given an opportunity to master different formal techniques used to represent and evaluate reasoning under uncertainty; critically reflect on the successes and failings of each proposed account; and analyse the assumptions underlying each different proposal to represent or manage uncertainty.

• have learnt to think clearly and precisely;

• be able to present complicated reasoning in understandable ways;

• be able to foster attention to detail.

Two assignments comprising a selection of short-answer problem sets 20% an 22% (due in the first half of the semester and in the second half respectively), a final 2-hour examination 50% (due at the end of the semester) and tutorial presence and participation 3%.

A set of course notes will be made available at the start of the semester.